Let's focus on some more interesting topic. I promised earlier to shed some light on the mechanisms to use instrument correlations to improve hedging across layers.
For instance, if we are trading TNA and TZA, since the general behavior of one of the two is pretty much determined by the other one, it's clear that it can be useful for an automated trading algo to balance the exposures of correlated assets.
To this purpose, I have defined for each Instrument, say I, the following quantities:
SAE(I) := "Signed (Volatility-Adjusted) Exposure"
REC(I) := "Relative Exposure of Correlated Instruments"
Such quantities are defined as follows:
SAE(I) := Closing Price * Position with sign * Multiplier * Volatility * 0.001 (so, say with $K as unit of measure)
[clearly, may multiply by 0.00001, if annualized volatility is in %]
for instance, an instrument could have an exposure of 15.56K, and so on.
While, the "
Relative Exposure of Correlated Instruments" is defined as:
Where corr(I,J) indicates your preferred correlation (or "codirection") metrics (such as for instance the SCX, we have seen previously).
This quantity, along with the instrument exposure SEA(I) is useful to rebalance exposure across layers, for instance, according to the following scheme:
The meaning of the schema seems intuitive.
Let's consider, for instance, SAE(I) > 0 and REC(I) > 0. In this case, both the instrument I and the set of correlated instruments C(I) have a positive exposure. So a SELL order of I would have an "hedging" effect on the exposure.
Let's consider for instance SAE(I) < 0 and REC(I) > 0. In this case, I has "negative" exposure (it has a short position), while the correlated instruments are "contrasting" this exposure (either through opposite position under positive correlation or same side position under negative correlation). Now, depending on which of the 2 exposure is larger (REC(I) or SAE(I)), we have an exposure reduction either by Selling of Buying (respectively) I. The other 2 cases are analogous.
Similarly, they offer an indication of the "role" of I within the folio. For instance, if SAE(I) > 0 and REC(I) < 0 and |SAE(I)| < |REC(I)| we can interpret the instrument I as having an "hedging value" within the folio and that it's suitable for (signed) position increase. The interpretations of the other cases, can be done applying a similar logic.
Let me know if you see improvements or errors, so I can fix them.